Early in this century, the Austrian mathematician J. Radon demonstrated that a two-dimensional slice of a three-dimensional object may be reproduced from the set of all of its projections. Computed tomography ("CT") X-ray systems generate a set of X-ray beam projections through an object to be examined. The resultant detected X-ray data are computer processed to reconstruct a tomographic image-slice of the object.
CT systems subject the object under examination to one or more pencil-like X-ray beams from all possible directions. The X-ray data may be generated in fan beam format (as is the case for the present invention), or in parallel beam format. In a fan beam system, the X-rays radiate from a source and are collected in a fan. By contrast, in a parallel beam system the X-rays are all parallel within a view. In either system, a view is one projection of the object onto the detectors, and a scan is a collection of all of the views.
In a fan beam scanning electron beam system such as described in U.S. Pat. No. 4,521,900 to Rand, or U.S. Pat. No. 4,352,021 to Boyd, an electron beam is produced by an electron gun and is accelerated downstream along the z-axis of an evacuated chamber. Further downstream a beam optical system deflects the electron beam into a scanning path, typically about 210.degree.. The deflected beam is then focussed upon a suitable target, typically a large arc of tungsten material, which produces a fan beam of X-rays.
The emitted X-rays penetrate an object (e.g., a patient) that is disposed along the z-axis and lying within a so-called reconstruction circle. X-ray beams passing through the object are attenuated by various amounts, depending upon the nature of the object traversed (e.g., bone, tissue, metal). One or more X-ray detectors, disposed on the far side of the object, receive these beams and provide signals proportional to the strength of the incoming X-rays.
Typically the output data from the detectors are processed using a filtered back-projection algorithm. Detector data representing the object scanned from many directions are arranged to produce image profiles for each scan direction. Since the X-rayed object is not homogeneous, these profiles will vary in intensity with the amount of radiation detected by the various detectors on the various scans. The rays from the various projections are then superimposed, or back-projected, to produce a computed tomographic image of the original object. The thus processed data are used to produce a reconstructed image of a slice of the object, which image may be displayed on a video monitor.
Systems similar to what is described in the above patents to Rand or Boyd are manufactured by Imatron, Inc., located in South San Francisco, Calif. These systems are termed "short scan" because the views used for reconstructing an object image cover 180.degree. plus the fan beam angle (about 30.degree.), e.g., about 210.degree. total, rather than a full 360.degree..
In these systems, the X-ray detectors also span 180.degree. plus the fan angle, and define a first plane that is orthogonal to the z-axis. The source of the X-rays scans or travels within a second plane, also orthogonal to the z-axis, but not necessarily coincident with the first plane. However in scanning electron beam fourth-generation CT systems, the large evacuated chamber and distance separating the target and detectors, can result in these two planes being offset by a dimension .DELTA.z, that may be in the range of a cm or so. Thus, while ideally reconstruction creates an image in a plane perpendicular to the z-axis using views acquired within that plane, due to the cone angle, each acquired view is not perpendicular to the z-axis.
This .DELTA.z offset causes the X-ray beam to somewhat misalign and sweep out a shallow cone during a scan, and unless the cone beam geometry is accounted for during reconstruction, cone beam error results. Unless corrected, cone beam error produces a reconstructed image that includes unwanted cone beam artifacts that appear as streaks in the reconstructed, displayed image.
To display a reconstructed image of the object slice requires computer intensive reconstruction techniques. Computed tomography is the method of determining the cross section of an X-rayed object by using projections of the object from many different angles. A mathematical reconstruction algorithm is used to reconstruct the object's cross section from the fan beam projections, represented by the detected data.
Computed tomography reconstruction algorithms exist for fan beam data and for parallel beam data. Such fan beam algorithms are described, for example, in "Principles of Computerized Tomographic Imaging" by Avinash Kak and Malcolm Slaney, IEEE Press, N.Y. (1987). The reference "Optimal Short-Scan Convolution Reconstruction for Fan Beam CT" by Dennis Parker, Med Phys., 9:254-257 (1982), describes weights used in short scan fan beam algorithms.
In general, attempting to process fan beam data in real time, e.g., a few seconds or less, requires using custom designed computer equipment. This results because fan beam reconstruction techniques involve spatial domain backprojection algorithms, which are extremely computer intensive in that many computational operations are required. Thus, generally, fan beam reconstruction is less desirable than parallel beam reconstruction.
By contrast, there exist parallel beam reconstruction techniques that use transform domain algorithms that execute rapidly using conventional computer array processors. Relying upon customized backprojection equipment is not desirable because a modification of the CT system can require modification of the backprojection equipment, a costly and time consuming process. Further, relatively few companies produce custom designed backprojectors, and from an engineering and business standpoint, it is undesirable for the CT system manufacturer to rely on sole-source equipment such as backprojectors.
It is therefore preferred that parallel beam reconstruction techniques be practiced, for reasons of speed and for ease of implementation using commercially available array processors. Among parallel beam reconstruction techniques are the so-called gridding Fourier inversion algorithms, wherein each view is transformed, convolved with a gridding function, and then added into a two-dimensional Fourier transform of the image. If such method is done for but one view, the resulting image equals the backprojection of that view, using a filtered backprojection algorithm. See, for example, J. D. O'Sullivan, "A Fast Sinc Function Gridding Algorithm for Fourier Inversion in Computer Tomography" IEEE Trans on Medical Imaging, vol. MI-4, no. 4, pp 200-207, December, 1985, and J. Jackson, C. Meyer, D. Nishimura, A. Macovski, "Selection of a Convolution Function for Fourier Inversion Using Gridding" IEEE Trans on Medical Imaging, vol MI-10, no. 3, pp 473-478. Another parallel beam algorithm was disclosed in M. Tabei, M. Ueda, "Backprojection by Unsampled Fourier Series Expansion and Interpolated FFT", IEEE Trans on Image Proc., vol. 1, No. 1, pp 77-87, a gridding technique, where a Gaussian gridding function was used, as such functions may be calculated rapidly on the fly.
While Tabei-type parallel beam reconstruction algorithms have many advantages, they cannot be used with fan beam data. Fortunately, however, so-called rebinning techniques are known for transforming or converting fan beam data to parallel beam data, whereupon fast parallel beam algorithms such as that disclosed by Tabei may be used for reconstruction. One such rebinning algorithm is described by Gabor Herman, in Image Reconstructions from Projections, 1980 Academic Press, N.Y.
However, even if fan beam data are suitably rebinned for reconstruction using a fast parallel beam reconstruction algorithm, the .DELTA.z offset noted above produces a so-called cone beam artifact in the reconstructed image. Further, conventional short scan fan beam to parallel beam rebinning techniques discard redundant data appearing at the top and bottom of the fan beam sinogram. This practice is undesirable because, in medical applications, the redundant regions of the sinogram represent data for which the patient was irradiated. Further, discarding the redundant data reduces the signal to noise ratio.
What is needed is a method of retaining redundant data in a fan beam sinogram during a rebinning operation. Preferably such modified rebinning method would make the resultant parallel beam data suitable for correcting cone beam error.
Further, there is a need for a modified Tabei-type algorithm capable of correcting for cone beam error, and capable of permitting imaging zooming on the displayed image from a point other than the center of the image. What is needed is a reconstruction method that permits a zoom view of the reconstructed image, from any point on the image.
The present invention describes such a modified rebinning procedure, and a modified Tabei-type parallel beam reconstruction procedure, whereby cone beam error is substantially reduced. Further, the present invention provides non-center zooming of the reconstructed displayed image. Further, the present invention may be implemented with conventional array processors, and is faster executing than the Tabei reconstruction method.